Ferenc, (01)
When I don't mention something, please don't make any assumptions
about what I might have said. (02)
JFS
>> The point I have been repeating in different ways is that there is
>> no such thing as an ideal upper level. Many people have reached
>> that conclusion after working very hard to find one. (03)
FK
> FK What you are saying then is that there are no numbers (forms to
> recognize), and we cannot divide the world into finite and infinite
> chunks and that there is no reflection on time and space. (04)
No. I said there is no *ideal* upper level. But there is an infinity
of *possible* upper levels. Some of them are undoubtedly better than
others, but we have no way of knowing which, if any, is the best
(or even which, if any, are sufficient for practical purposes). (05)
The recommendation I proposed in my 2000 book, in many published
papers, and in many, many emails follows from that point: (06)
1. Use a loosely organized hierarchy of the terminology for each
and every natural language you want to support. (07)
2. Provide a framework that can accommodate as many formal theories
and microtheories for every specialized domain of knowledge that
anyone might ever define or imagine. (08)
3. Provide a theory supported with suitable tools for relating
all those theories to one another and to the terminologies
for each NL. (09)
4. And by the way, those theories and microtheories mentioned
in point #2 happen to be elements of a Lindenbaum lattice.
(This point is not a proposal that I am making. It happens
to be a theorem that Lindenbaum proved over 80 years ago.) (010)
5. The lattice of point #4 can provide a method for organizing
all those theories and supporting systematic methods for
revising them, generalizing them, and specializing them. (011)
> Because the point is not what you call the semantic primitives, but that
> you experience them a) through perception, b) reflection (thinking)... (012)
I'm not making any assumptions about primitives or about any methods
of experience, perception, or reflection. The method outlined in
points #1 to #5 can support any or all theories of primitives and
any psychological evidence that anyone might ever discover. (013)
For some related linguistic issues, following is a slightly edited
note that I sent to Corpora list. (014)
John (015)
 Original Message 
Subject: Re: [CorporaList] TextGraphs6 and semantic networks
Date: Sun, 13 Mar 2011 14:09:05 0500
From: John F. Sowa
To: corpora@xxxxxx (016)
> The bottleneck currently is how can we get the highprecision results of
> coreference resolution to build completed Conceptual Graphs from texts. (017)
That is the bottleneck that has plagued every version of formal
semantics from Montague to the present. Logicians publish papers
with toy sentences like "John seeks a unicorn". But the fatal flaw
is that they usually assume Frege's principle: (018)
The meaning of a sentence is completely determined
by the meaning of its symbols and the syntax for
combining those symbols. (019)
Natural languages violate Frege's constraint in multiple ways.
In general, the meaning of a sentence depends critically on context
dependent factors, such as the time and place of utterance, the
speaker (or writer), the listener (or reader), their background
knowledge, their intentions, the speaker's guess about the listener's
knowledge and intentions, the listener's guess about the speaker, etc. (020)
Linguists and logicians have published many excellent analyses
of each of those issues. But NL texts that occur "in the wild"
violate Frege's principle in many different and highly creative
ways  sometimes several different ways in a single sentence. (021)
One of the famous epigrams of programming by Alan Perlis: (022)
"One can't proceed from the informal to the formal by formal means." (023)
There are some wellwritten texts that are sufficiently precise that
they can be translated to a formal logic. For example, Naproche
(NAturallanguage PROof CHEcker) maps a mathematical proof stated
in English to logic and checks the proof ( http://naproche.net/ ). (024)
What makes that English precise is that the author (a mathematician)
(1) has a precise formal semantics in mind and (2) makes an effort
to describe it clearly. Very few texts meet both of those criteria. (025)
Programming languages are just as formal as mathematics, but programmers
are notoriously lazy about documenting what they do in any language.
When they do, the results look like Slide 27 in the talk I mentioned: (026)
http://www.jfsowa.com/talks/pursue.pdf (027)
That language cannot be translated to the formal language of the
original program (COBOL, in this case). However, if you *start*
with the COBOL and map it to a formal notation (in this case to
conceptual graphs), you can generate precise, formal graphs. (028)
With the usual methods of NLP, you can map informal English to graphs
that are just as informal as the English. Then with suitable graph
matching algorithms, you can find an approximate match of the informal
graphs to the formal graphs (assuming, of course, that you have some
independent source for the formal graphs  and that's a very big
assumption that is often difficult or impossible to satisfy). (029)
Note that this method does not violate the epigram by Perlis:
the precision does *not* come from English, but from COBOL
(or some other source for the formal graphs). (030)
> As my understanding, you build an index for conceptual graphs.
> Does this method work for subgraph matching? (031)
Yes. There are many different, but related algorithms for doing
such indexing and searching. I cited some based on methods for
chemical graphs. Those applications *require* searching and
finding subgraphs. (032)
For pharmaceutical applications, they want to find chemicals that
have the same active subgraph (the critical part for some drug) but
may have different molecular structures attached to that subgraph.
That's very similar to the requirements for NLP. (033)
John (034)
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